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arXiv:1404.6848 · New Journal of Physics

Topological phase transition in the quench dynamics of a one-dimensional Fermi gas with spin–orbit coupling

Pei Wang, Wei Yi, Gao Xianlong

Published Jan 15, 2015• 11 citations
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Abstract

We study the quench dynamics of a one-dimensional ultracold Fermi gas with synthetic spin-orbit coupling. At equilibrium, the ground state of the system can undergo a topological phase transition and become a topological superfluid with Majorana edge states. As the interaction is quenched near the topological phase boundary, we identify an interesting dynamical phase transition of the quenched state in the long-time limit, characterized by an abrupt change of the pairing gap at a critical quenched interaction strength. We further demonstrate the topological nature of this dynamical phase transition from edge-state analysis of the quenched states. Our findings provide interesting clues for the understanding of topological phase transitions in dynamical processes, and can be useful for the dynamical detection of Majorana edge states in corresponding systems.

DOI
10.1088/1367-2630/17/1/013029

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We study the quench dynamics of a one-dimensional ultracold Fermi gas with synthetic spin-orbit coupling. At equilibrium, the ground state of the system can undergo a topological phase transition and become a topological superfluid with Majorana edge states. As the interaction is quenched near the topological phase boundary, we identify an interesting dynamical phase transition of the quenched state in the long-time limit, characterized by an abrupt change of the pairing gap at a critical quenched interaction strength. We further demonstrate the topological nature of this dynamical phase transition from edge-state analysis of the quenched states. Our findings provide interesting clues for the understanding of topological phase transitions in dynamical processes, and can be useful for the dynamical detection of Majorana edge states in corresponding systems.
The spin–orbit-coupled degenerate Fermi gas provides a new platform for realizing topological superfluids and related topological excitations. However, previous studies have been mainly focused on the topological properties of the stationary ground state. Here, we investigate the quench dynamics of a spin–orbit-coupled two-dimensional Fermi gas in which the Zeeman field serves as the major quench parameter. Three post-quench dynamical phases are identified according to the asymptotic behaviour of the order parameter. In the undamped phase, a persistent oscillation of the order parameter may support a topological Floquet state with multiple edge states. In the damped phase, the magnitude of the order parameter approaches a constant via a power-law decay, which may support a dynamical topological phase with one edge state at the boundary. In the overdamped phase, the order parameter decays to zero exponentially although the condensate fraction remains finite. These predictions can be observed in the strong-coupling regime. Spin–orbit-coupled Fermi gases have been shown to support exotic topological quantum states. Here, the authors investigate quench dynamics of these gases in two dimensions, and find that three different phases with different topological properties emerge depending on the behaviour of the order parameter.
We demonstrate that non-equilibrium dynamics provides a direct means of detecting the topological phase transition (TPT) between conventional and topological superfluid (SF) phases in one-dimensional spin-orbit-coupled Fermi gases with attractive interactions. To date, no cold atom experiment has realized a topological SF, because of loss or heating processes. In the alkali fermions, off-resonant light scattering dominates these processes, therefore, we minimize their impact by rapidly quenching in and out of the topological SF phase. This quench excites Bogoliubov quasiparticles in the final phase (a conventional SF), the distribution of which carries signatures of the TPT. We calculate the resulting spin-resolved momentum distribution by self-consistently solving the time-dependent Bogoliubov-de Gennes equations. They exhibit Kibble-Zurek scaling and St\{u}ckelberg oscillations characteristic of the TPT. We discuss parameter regimes where the TPT is experimentally accessible.
We show that pairing in an ultracold Fermi gas under spin-orbital-angular-momentum coupling (SOAMC) can acquire topological characters encoded in the quantized angular degrees of freedom. The resulting topological superfluid is the angular analog of its counterpart in a one-dimensional Fermi gas with spin-orbit coupling, but characterized by a Zak phase defined in the angular-momentum space. Upon tuning the SOAMC parameters, a topological phase transition occurs, which is accompanied by the closing of the quasiparticle excitation gap. Remarkably, a topological vortex state can also be stabilized by deforming the Fermi surface, which is topologically nontrivial in both the coordinate and angular-momentum space, offering interesting potentials for applications in quantum information and quantum control. We discuss how the topological phase transition and the exotic vortex state can be detected experimentally.
The twodimensional chiral p-wave superfluid is known to be topological, with gapless Majorana states expected to exist at its edge. The possibility to utilise such Majorana excitations as fault-tolerant quantum bits has spurred interest in robust experimental realisation of such systems. One proposed pathway is to use spin-orbit coupled and spin-imbalanced ultracold gases of fermionic atoms subject to conventional s-wave pairing, as inducing a large-enough Zeeman energy splitting between pseudo-spin-1/2 states drives the system into a topological superfluid (TSF) phase with chiral-p-wave characteristics. In this thesis, we apply and extend advanced theoretical methods to study this topological phase transition in detail. Specifically, our work elucidates what happens when the s-wave interaction strength between atoms is increased so that the system undergoes the BCS-to-BEC crossover. While previous studies have largely focused on the weakly interacting BCS regime, studying the full crossover reveals new properties of the TSF phase that may aid its experimental realisation in the future. In particular, we obtain phase diagrams in the parameter space of the s-wave interaction strength and Zeeman energy. As long as the system is in the nontopological superfluid (NSF) phase, it shows the ordinary features expected during the BCS-to-BEC crossover, such as the shrinking and disappearance of the Fermi surfaces as the s-wave interaction strength is increased. The TSF phase, however, exhibits strikingly different behavior: it retains the BCS-limit characteristics of a TSF even as the s-wave interaction strength reaches extremely large values. The phase diagrams we obtain also show that increasing the s-wave interaction strength changes the nature of the topological transition from second-order continuous to first-order. During the first-order topological transition, the system splits into coexisting regions of NSF and TSF phases. We study this phase coexistence theoretically and obtain analytical formulae that capture the behaviour of all relevant thermodynamic quantities during the first-order topological transition. In that, our work extends current fundamental knowledge about spin-imbalanced Fermi gases to situations with finite spin-orbit coupling. We also investigate the gapless edge states emerging at the system’s boundaries, as these are crucial for experiments that aim to observe topological phases and realise novel quantum-information-processing architectures. The principle of bulk-boundary correspondence guarantees that gapless Majorana excitations should be localised to the interface between coexisting NSF and TSF regions. We develop a detailed theoretical description of this novel topological interface state and compare its physical features with those exhibited by the Majorana states expected to exist at the system’s boundary with vacuum.
Based on density matrix renormalization group method, we investigate the spin-orbit coupled Fermi gas with attractive interactions in one-dimensional optical lattice and present a complete phase diagram for a quarter-filling system with intermediate strong interactions. We unveil the exotic pairings induced by spin-orbit couplings and the phase transitions between different pairing states, and further demonstrate the existence of the long-sought topological superfluid state at moderate magnetic field and spin-orbit coupling strength. For the particle conserved system, this topological superfluid state can be fixed by its gapless single particle excitation, Luttinger parameter and non-trivial boundary effect. Our study removes out the widespread doubt on the existence of topological superfluid in one dimension and paves the way for simulating topological superfluid states in cold atom settings.
We theoretically study trapped one-dimensional Fermi gases in the presence of spin-orbit coupling induced by Raman lasers. The gas changes from a conventional (nontopological) superfluid to a topological superfluid as one increases the intensity of the Raman lasers above a critical chemical-potential-dependent value. Solving the Bogoliubov-de Gennes equations self-consistently, we calculate the density of states in real and momentum space at finite temperatures. We study Majorana fermions (MFs) which appear at the boundaries between topologically trivial and topologically nontrivial regions. We linearize the trap near the location of a MF, finding an analytic expression for the localized MF wave function and the gap between the MF state and other edge states.